1. Field of the Invention
This invention relates generally to a method and apparatus for determining the horizontal and vertical resistivities and the relative dip angle of a borehole in an electrically anisotropic earth formation. More specifically, this invention relates to an electromagnetic wave induction technique for measuring resistivity using a tool having an antenna that is disposed within a plane which is inclined with respect to a plane that is normal to the axis of the tool. This invention also relates to a method and apparatus for steering a downhole tool during a drilling operation in order to maintain the borehole within a desired earth formation.
2. Description of the Related Art
In the field of petroleum well drilling and logging, electromagnetic wave resistivity sensors are frequently used to provide an indication of the electrical resistivity of rock formations surrounding an earth borehole. Such information regarding resistivity is useful in ascertaining the presence or absence of hydrocarbons. A typical electromagnetic wave resistivity tool comprises a transmitter antenna and a pair of receiver antennas located at different distances from the transmitter antenna along the axis of the tool. The transmitter antenna is used to transmit electromagnetic waves into the surrounding formation. In turn, the magnetic field in the formation induces an electrical voltage in each receiver antenna. Due to geometric spreading and absorption by the surrounding earth formation, the induced voltages in the two receiving antennas have different phases and amplitudes. Experiments have shown that the phase difference (Φ) and amplitude ratio (attenuation, A) of the induced voltages in the receiver antennas are indicative of the resistivity of the formation. The point in the formation (as defined by a radial distance from the tool axis) to which such a resistivity measurement pertains is a function of the frequency of the transmitter and the distance from the transmitter to the mid-point between the two receivers. Thus, one may achieve multiple radial depths of investigation of resistivity either by providing multiple transmitters at different distances from the receiver pair or by operating a single transmitter at multiple frequencies.
If a formation is electrically isotropic, the resistivities measured at the various depths of investigation by such an electromagnetic wave resistivity tool will be the same. However, if the resistivities corresponding to the various depths of investigation are different, such differences indicate that the formation being measured is electrically anisotropic. In electrically anisotropic formations, the anisotropy is generally attributable to extremely fine layering during the sedimentary build-up of the formation. Hence, in a formation coordinate system oriented such that the x-y plane is parallel to the formation layers and the z axis is perpendicular to the formation layers, resistivities Rx and Ry in directions x and y, respectively, are the same, but resistivity Rz in the z direction is different from Rx and Ry. Thus, the resistivity in a direction parallel to the plane of the formation (i.e., the x-y plane) is known as the horizontal resistivity, Rh, and the resistivity in the direction perpendicular to the plane of the formation (i.e., the z direction) is known as the vertical resistivity, Rv. The index of anisotropy, α, is defined as α=[Rv/Rh]1/2.
The relative dip angle, θ, is the angle between the borehole axis (tool axis) and the normal to the plane of the formation. If the axis of an electromagnetic wave resistivity tool is perpendicular to the plane of an anisotropic formation (i.e., θ=0°), both the phase shift and amplitude attenuation measurements reflect only the horizontal resistivity. However, if the axis of the tool is inclined with respect to the normal of the formation plane (i.e., for non-zero relative dip angle), the rock anisotropy affects the resistivity derived from phase shift measurements (“phase shift resistivity” or RΦ) differently than it affects the resistivity derived from amplitude attenuation measurements (“amplitude attenuation resistivity” or RA). For small relative dip angles (e.g., θ less than about 45°), the difference between phase shift and amplitude attenuation resistivities is relatively small. However, this difference becomes significant for relative dip angles greater than about 50°, and the difference is large for horizontal boreholes (i.e., θ=90°).
Before the present invention, practitioners in the art have used a number of techniques to determine the anisotropy of earth formations, most of which involve the use of coil antennas to measure resistivity. However, each of the existing techniques suffers from one or more disadvantages. For example, U.S. Pat. No. 4,980,643, issued Dec. 25, 1990 to Gianzero and Su, teaches the use of additional receiver coils oriented differently from (not co-axial with) conventional receiver coils to detect skew signals induced by skewness in the magnetic field pattern in the presence of asymmetrical formations. The axis of such additional receiver coils according to the '643 patent is preferably orthogonal to that of the conventional receiver coils, which are co-axial with the tool axis. However, such orthogonal coil (antenna) configurations are not generally considered practical for a measuring while drilling (MWD) or logging while drilling (LWD) tool because, if the coil is located in the interior of the tool, the presence of the coil necessitates a non-conventional mud flow path and decreases the mechanical strength of the tool. If, on the other hand, the additional coil is located on the exterior of the tool, the coil is susceptible to damage by formation cuttings in the return mud flow.
Similarly, U.S. Pat. No. 5,329,448, issued Jul. 12, 1994 to Rosthal, discloses a method and apparatus for determining the horizontal and vertical resistivities of an earth formation using an iterative error minimization technique. However, the '448 patent, which discloses a conventional antenna configuration in which the transmitter and receiver coils are aligned co-axially with the tool, does not provide a way to determine the relative dip angle. Instead, the relative dip angle must be obtained from another measurement source or from prior knowledge of the formation. Likewise, U.S. Pat. No. 5,656,930, issued Aug. 12, 1997 to Hagiwara, discloses a method for determining the anisotropic properties of subterranean formations comprising thinly laminated sand/shale sequences using an induction logging tool. However, like the '448 patent, the method of the '930 patent requires the derivation of the relative dip angle from another measurement.
In a technical paper entitled “A New Method to Determine Horizontal Resistivity in Anisotropic Formations Without Prior Knowledge of Relative Dip,” 37th SPWLA 37th Annual Logging Symposium, New Orleans, Jun. 16-19, 1996, Hagiwara discloses a method to determine the horizontal resistivity for deviated boreholes or dipping formations using two conventional induction-type resistivity measurements. However, Hagiwara's method does not provide the relative dip angle. To obtain the relative dip angle, the formation anisotropy must be known. Moreover, Hagiwara showed that, for conventional induction logging tools (in which the transmitter and receiver antennas are oriented co-axially with the tool), it is impossible to obtain all three parameters (horizontal resistivity, vertical resistivity, and relative dip angle) simultaneously. The reason such a simultaneous solution is not possible using conventional induction logging tools is that, in the response of such tools, the vertical resistivity and the relative dip angle are coupled (i.e., they are not independent).
In European Patent Application No. 97118854.5 by Wu, published May 6, 1998, Wu discloses a method and apparatus for determining horizontal conductivity, vertical conductivity, and relative dip angle during a drilling operation. If the relative dip angle is unknown, Wu's technique involves the formulation of a relationship between the dielectric constants of the formation to the anisotropic conductivities of the formation. However, in the proof by Hagiwara mentioned above, the dielectric constants are assumed quantities, and their contribution to the phase shift resistivity is minimal. Therefore, even if the dielectric constants are known, the vertical resistivity and the relative dip angle are still coupled and do not allow for a simultaneous solution.
It would, therefore, be a significant advancement in the art to provide an improved method and apparatus for simultaneously determining the horizontal resistivity, vertical resistivity, and relative dip angle in a MWD or LWD mode of operation.
Furthermore, to maximize the production of hydrocarbons from a petroleum well, it would be beneficial to steer the drilling apparatus with respect to geological bed boundaries in order to maintain the borehole within a desired hydrocarbon-bearing earth formation or “payzone.” As discussed by Luling in U.S. Pat. No. 5,241,273, when conventional resistivity tools traverse geological bed boundaries between formations having different resistivities, the responses of such tools exhibit horns at the bed boundaries. Before the advent of the method disclosed by Luling, practitioners in the art considered such horns to be unfortunate anomalies and sought ways to eliminate the horns. By contrast, Luling recognized the value of such horns and disclosed a method of utilizing the horns to assist with directional drilling. However, Luling teaches the use of conventional transmitter and receiver antennas oriented in planes orthogonal to the tool axis, and such conventional resistivity tools produce the same type of horn response regardless of whether the tool travels from a region of lower resistivity to higher resistivity or from a region of higher resistivity to lower resistivity. Consequently, as a conventional resistivity tool approaches a bed boundary between a first bed having one resistivity and a second bed having a different resistivity, Luling's method indicates only the presence of the boundary; Luling's method does not provide an early indication of whether the resistivity of the second bed is higher or lower than that of the first bed. Only after the tool crosses the boundary and travels a sufficient distance into the second bed will Luling's method provide an indication as to whether the resistivity increased or decreased so that the driller can make a decision regarding which bed is more desirable. As a result, Luling's method may lead to unnecessary penetrations into undesirable beds.
In U.S. Pat. No. 5,230,386, Wu and Wisler disclose another method of maintaining a drillstring in a certain formation during a directional drilling operation using an electromagnetic propagation resistivity sensor. However, the method of Wu and Wisler requires a reference resistivity log with which to compare the readings of the resistivity sensor in the directional drilling operation. The reference resistivity log is obtained by drilling and logging an offset vertical well near the location of the desired directional well or by creating an assumed log based on known geological information concerning the area of interest. The method of Wu and Wisler involves significant drawbacks in terms of the time, expense, and uncertainty associated with such a reference resistivity log.
A technical paper entitled “A New Generation of Electrode Resistivity Measurements for Formation Evaluation While Drilling,” by Bonner et al., SPWLA 35th Annual Logging Symposium, Jun. 19-22, 1994, discloses a focused electrode resistivity tool that is azimuthally sensitive and could be used to steer a drillstring during a directional drilling operation. However, such electrode resistivity tools operate by forcing electric current into an earth formation by direct conduction, which requires conductive mud. Consequently, such electrode resistivity tools will not function properly in oil-based mud or in the presence of resistive invasion.
U.S. Pat. No. 5,508,616 to Sato et al. discloses an induction logging method and apparatus for determining the electric conductivity distribution of an earth formation in the circumferential direction about the borehole. The apparatus of the '616 patent employs transmitter and receiver coils that are disposed along the tool axis in a manner such that the coils face each other in an inclined fashion at symmetric angles. Although the '616 apparatus provides directional sensitivity which may be helpful in steering a drilling tool, the '616 patent does not teach how to utilize a transmitter and a receiver oriented at arbitrary inclination angles with respect to each other in order to take advantage of the special characteristics of the horns in the resulting response.
In light of the foregoing limitations, it would also be a significant advancement in the art to provide an improved method and apparatus for steering a downhole tool during a directional drilling operation in order to maintain the borehole within a desired earth formation by providing an advance indication of the resistivity of a given formation before entry into the formation. Such an improved method and apparatus would not require an offset vertical well or an assumed reference resistivity log and would be functional in oil-based or water-based mud and conditions of resistive or conductive invasion.